Potenciación

Simplifique la expresión y elimine los exponentes negativos.

  1. a9a−5\hspace{0.1cm}a^9a^{-5}\\[0.3cm]
  2. (3y2)(4y5)\hspace{0.1cm}\left(3y^2\right)\left(4y^5\right)\\[0.3cm]
  3. (12x2y4)(12x5y)\hspace{0.1cm}\left(12x^{2}y^{4}\right)\left({\dfrac{1}{2}}x^{5}y\right)\\[0.3cm]
  4. (6y)3\hspace{0.1cm}\left(6y\right)^{3}\\[0.3cm]
  5. x9(2x)4x3\hspace{0.1cm}\dfrac{x^{9}\left(2x\right)^{4}}{x^{3}}\\[0.3cm]
  6. a−3b4a−5b5\hspace{0.1cm}\dfrac{a^{-3}b^{4}}{a^{-5}b^{5}}\\[0.3cm]
  7. b4(12b2)(12b−8)\hspace{0.1cm}b^{4}\left(\dfrac{1}{2}b^{2}\right)\left(12b^{-8}\right)\\[0.3cm]
  8. (2s3t−1)(14s6)(16t4)\hspace{0.1cm}\left(2s^{3}t^{-1}\right)\left(\dfrac{1}{4}s^{6}\right)\left(16t^{4}\right)\\[0.3cm]
  9. (rs)3(2s)−2(4r)4\hspace{0.1cm}\left(rs\right)^{3}\left(2s\right)^{-2}\left(4r\right)^{4}\\[0.3cm]
  10. (2u2v3)3(3u3v)−2\hspace{0.1cm}\left(2u^{2}v^{3}\right)^{3}\left(3u^{3}v\right)^{-2}\\[0.3cm]
  1. (6y3)42y5\hspace{0.1cm}\dfrac{\left(6y^{3}\right)^{4}}{2y^{5}}\\[0.3cm]
  2. (2x3)2(3x4)(x3)4\hspace{0.1cm}\dfrac{\left(2x^{3}\right)^{2}\left(3x^{4}\right)}{\left(x^{3}\right)^{4}}\\[0.3cm]
  3. (x2y3)4(xy4)−3x2y\hspace{0.1cm}\dfrac{\left(x^{2}y^{3}\right)^{4}\left(xy^{4}\right)^{-3}}{x^{2}y}\\[0.3cm]
  4. (c4d3cd2)(d2c3)3\hspace{0.1cm}\left(\dfrac{c^{4}d^{3}}{cd^{2}}\right)\left(\dfrac{d^{2}}{c^{3}}\right)^{3}\\[0.3cm]
  5. (xy2z3)4(x3y2z)3\hspace{0.1cm}\dfrac{\left(xy^{2}z^{3}\right)^{4}}{\left(x^{3}y^{2}z\right)^{3}}\\[0.3cm]
  6. (xy−2z−3x2y3z−4)−3\hspace{0.1cm}\left(\dfrac{xy^{-2}z^{-3}}{x^{2}y^{3}z^{-4}}\right)^{-3}\\[0.3cm]
  7. (q−1rs−2r−5sq−8)−1\hspace{0.1cm}\left(\dfrac{q^{-1}rs{-2}}{r^{-5}sq^{-8}}\right)^{-1}\\[0.3cm]
  8. (3ab2c)(2a2bc5)−2\hspace{0.1cm}\left(3ab^{2}c\right)\left(\dfrac{2a^{2}b}{c^{5}}\right)^{-2}\\[0.3cm]

Simplifique las siguientes expresiones y elimine los exponentes negativos.

  1. x23y15\hspace{0.1cm}x^{\frac{2}{3}}y^{\frac{1}{5}}\\[0.3cm]
  2. (2x32)(4x)−12\hspace{0.1cm}\left(2x^{\frac{3}{2}}\right)\left(4x\right)^{-\frac{1}{2}}\\[0.3cm]
  3. (−3a14)(9a)−32\hspace{0.1cm}\left(-3a^{\frac{1}{4}}\right)\left(9a\right)^{-\frac{3}{2}}\\[0.3cm]
  4. (−2a34)(5a32)\hspace{0.1cm}\left(-2a^{\frac{3}{4}}\right)\left(5a^{\frac{3}{2}}\right)\\[0.3cm]
  5. (4b)12(8b25)\hspace{0.1cm}\left(4b\right)^{\frac{1}{2}}\left(8b^{\frac{2}{5}}\right)\\[0.3cm]
  6. (8x6)−23\hspace{0.1cm}\left(8x^{6}\right)^{-\frac{2}{3}}\\[0.3cm]
  7. (c2d3)−13\hspace{0.1cm}\left(c^{2}d^{3}\right)^{-\frac{1}{3}}\\[0.3cm]
  8. (4x6y8)32\hspace{0.1cm}\left(4x^{6}y^{8}\right)^{\frac{3}{2}}\\[0.3cm]
  9. (y34)23\hspace{0.1cm}\left(y^{\frac{3}{4}}\right)^{\frac{2}{3}}\\[0.3cm]
  10. (a25)−34\hspace{0.1cm}\left(a^{\frac{2}{5}}\right)^{-\frac{3}{4}}\\[0.3cm]
  11. (2x4y−45)3(8y2)23\hspace{0.1cm}\left(2x^{4}y^{-\frac{4}{5}}\right)^{3}\left(8y^{2}\right)^{\frac{2}{3}}\\[0.3cm]
  1. (x−5y3z10)−35\hspace{0.1cm}\left(x^{-5}y^{3}z^{10}\right)^{-\frac{3}{5}}\\[0.3cm]
  2. (x6yy4)52\hspace{0.1cm}\left(\dfrac{x^{6}y}{y^{4}}\right)^{\frac{5}{2}}\\[0.3cm]
  3. (−2x13y12z16)4\hspace{0.1cm}\left(\dfrac{-2x^{\frac{1}{3}}}{y^{\frac{1}{2}}z^{\frac{1}{6}}}\right)^{4}\\[0.3cm]
  4. (3a−24b−13)−1\hspace{0.1cm}\left(\dfrac{3a^{-2}}{4b^{-\frac{1}{3}}}\right)^{-1}\\[0.3cm]
  5. (y10z−5)15(y−2z3)13\hspace{0.1cm}\dfrac{\left(y^{10}z^{-5}\right)^{\frac{1}{5}}}{\left(y^{-2}z^{3}\right)^{\frac{1}{3}}}\\[0.3cm]
  6. (9st)32(27s3t−4)23\hspace{0.1cm}\dfrac{\left(9st\right)^{\frac{3}{2}}}{\left(27s^{3}t^{-4}\right)^{\frac{2}{3}}}\\[0.3cm]
  7. (a2b−3x−1y2)3(x−2b−1a32y13)\hspace{0.1cm}\left(\dfrac{a^{2}b^{-3}}{x^{-1}y^{2}}\right)^{3}\left(\dfrac{x^{-2}b^{-1}}{a^{\frac{3}{2}}y^{\frac{1}{3}}}\right)\\[0.3cm]
  8. (−2x13y12z16)4(2x−13y−12z−16)−4\hspace{0.1cm}\left(\dfrac{-2x^{\frac{1}{3}}}{y^{\frac{1}{2}}z^{\frac{1}{6}}}\right)^{4}\left(\dfrac{2x^{-\frac{1}{3}}}{y^{-\frac{1}{2}}z^{-\frac{1}{6}}}\right)^{-4}\\[0.3cm]

Radicación

Realice las siguientes operaciones y simplifique si es posible.

  1. 814\hspace{0.1cm}\sqrt [4] {81}\\[0.3cm]
  2. −83\hspace{0.1cm}\sqrt [3] {-8}\\[0.3cm]
  3. x43\hspace{0.1cm}\sqrt [3] {x^4}\\[0.3cm]
  4. 81x8y44\hspace{0.1cm}\sqrt [4] {81x^8y^4}\\[0.3cm]
  5. 32+200\hspace{0.1cm}\sqrt{32}+\sqrt{200}\\[0.3cm]
  6. 25b−b3\hspace{0.1cm}\sqrt{25b}-\sqrt{b^3}\\[0.3cm]
  7. 32+18\hspace{0.1cm}\sqrt{32}+\sqrt{18}\\[0.3cm]
  8. 965+35\hspace{0.1cm}\sqrt[5]{96}+\sqrt[5]{3}\\[0.3cm]
  9. −35965\hspace{0.1cm}\cfrac{\sqrt[5]{-3}}{\sqrt[5]{96}}\\[0.3cm]
  10. 64x63\hspace{0.1cm}\sqrt[3]{\sqrt{64x^6}}\\[0.3cm]
  1. a2b3⋅a4b3\hspace{0.1cm}\sqrt[3]{a^2b}\cdot\sqrt[3]{a^4b}\\[0.3cm]
  2. 484−34\hspace{0.1cm}\sqrt[4]{48}-\sqrt[4]{3}\\[0.3cm]
  3. x2173\hspace{0.1cm}\sqrt[3]{\sqrt[7]{x^{21}}}\\[0.3cm]
  4. x225\hspace{0.1cm}\sqrt{\dfrac{x^2}{25}}\\[0.3cm]
  5. 81a3b5c63\hspace{0.1cm}\sqrt[3]{81a^3b^5c^6}\\[0.3cm]
  6. 2x2y33⋅4xz33\hspace{0.1cm}\sqrt[3]{2x^2y^3}\cdot\sqrt[3]{4xz^3}\\[0.3cm]
  7. 10−40x4+90x4y8\hspace{0.1cm}\sqrt{10}-\sqrt{40x^4}+\sqrt{90x^4y^8}\\[0.3cm]
  8. −64273\hspace{0.1cm}\sqrt[3]{-\cfrac{64}{27}}\\[0.3cm]

Realice las siguientes operaciones y simplifique si es posible.

  1. a6b123\hspace{0.1cm}\sqrt[3]{\sqrt{a^6b^{12}}}\\[0.3cm]
  2. x3(x2y)2\hspace{0.1cm}\sqrt{x^3\sqrt{\left(x^2y\right)^2}}\\[0.3cm]
  3. (−−27xxy33)3\hspace{0.1cm}\left(-\sqrt[3]{-\cfrac{27x}{xy^3}}\right)^3\\[0.3cm]
  4. 38x3−18xy2+32x5\hspace{0.1cm}3\sqrt{8x^3}-\sqrt{18xy^2}+\sqrt{32x^5}\\[0.3cm]
  5. (−2x)3−z63\hspace{0.1cm}\sqrt[3]{\cfrac{\left(-2x\right)^3}{-z^6}}\\[0.3cm]
  6. 423−163\hspace{0.1cm}4\sqrt[3]{2}-\sqrt[3]{16}\\[0.3cm]
  7. 3203\hspace{0.1cm}\sqrt[3]{320}\\[0.3cm]
  8. a3⋅a\hspace{0.1cm}\sqrt[3]{a}\cdot\sqrt{a}\\[0.3cm]
  9. a4a23\hspace{0.1cm}\cfrac{\sqrt[4]{a}}{\sqrt[3]{a^2}}
  10. 9x−4y6\hspace{0.1cm}\sqrt{9x^{-4}y^6}\\[0.3cm]
  11. 81r5s84\hspace{0.1cm}\sqrt[4]{81r^5s^8}\\[0.3cm]
  1. x7y12125x4\hspace{0.1cm}\sqrt[4]{\cfrac{x^7y^{12}}{125x}}\\[0.3cm]
  2. 3t4v23⋅−9t−1v43\hspace{0.1cm}\sqrt[3]{3t^4v^2}\cdot\sqrt[3]{-9t^{-1}v^4}\\[0.3cm]
  3. (2u−3v4)66\hspace{0.1cm}\sqrt[6]{\left(2u^{-3}v^4\right)^6}\\[0.3cm]
  4. $\hspace{0.1cm}\sqrt[3]\cfrac{3x^2y^5}{4x}\\[0.3cm]$
  5. 8x3y45⋅4x4y25\hspace{0.1cm}\sqrt[5]{\cfrac{8x^3}{y^4}}\cdot\sqrt[5]{\cfrac{4x^4}{y^2}}\\[0.3cm]
  6. 5xy7⋅10x3y3\hspace{0.1cm}\sqrt{5xy^7}\cdot\sqrt{10x^3y^3}\\[0.3cm]
  7. x8(y−1)124\hspace{0.1cm}\sqrt[4]{x^8\left(y-1\right)^{12}}\\[0.3cm]
  8. x4y10\hspace{0.1cm}\sqrt{x^4y^{10}}\\[0.3cm]